Award for Multiresolution Growth and Flow

The thesis has been awarded with the ETH Medal for outstanding Doctoral Work. 

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Angiogenesis simulations make the cover of the Biophysical Journal

Our hybrid model of sprouting angiogenesis made the cover of the October issue of the Biophysical Journal.
The model uses a hybrid cellular-continuum representation of endothelial cells and for the first time an explicit model of the extra-cellular matrix. We present simulations which assess the effects of matrix density or the cleaving of matrix-bound growth factors such as VEGF.

See the Biophysical Journal web site for the full article »

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Vortex particles made the news...

articles about the simulation

Our simulation of trailing aircraft vortices made the news:
Article in the SonntagsZeitung (Switzerland)
Article in ScienceDaily

Cover article of ERCIM News

The movie: «The Secret Life of Vortices»

The article describing the simulation and the underlying technology was published in "Computer Methods
in Applied Mechanics and Engineering" [1].
We also made a short movie with "subtitles" relating to similar vortical flows.

[1] P. Chatelain, A. Curioni, M. Bergdorf, D. Rossinelli, W. Andreoni, and P. Koumoutsakos. Billion Vortex Particle direct numerical simulation of aircraft wakes. Comput. Methods Appl. Mech. Engrg., 197(13–16):1296–1304, 2008.
Link to publisher site.

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Mesoscale models of mesenchymal motion

..simulating the signaling and morphology of cells on the move.

Fig 1: Example of the structure of the artificial matrix in the model.

Fig 2: Simulation of sprouting angiogenesis: “mother” vessel on the left and migrating tips on the right-hand side.

Cell migration is a crucial element of embryogenesis and homeostatic processes such as the repair of injured tissues. Furthermore, it appears in numerous pathologies including vascular disease, tumor growth, metastasis, and the cancer-related formation of new lymphatic and blood vessel networks. The potential returns of understanding the underlying principles of cell migration are as pervasive as migration itself: they range from improvements in the manufacture of artificial tissues, new strategies for anti-angiogenic therapy, to restraining invasive tumors.
When cells migrate they are subjected to both complex biochemical and mechanical migration cues. In order to assess the effect of different cues on migration patterns or morphologies I developed a model which is based on a continuum representation of the cells, so the spatial distribution of cells is determined by a density function for each cell type. This approach renders implementations of this model efficient and scalable, therefore enabling the tackling of macroscopic 3D systems of migration. Cell density functions are approximated using smooth particle approximations, which allows the model to represent small cell clusters in a mesoscale manner. The use of particles also opens up the possibility to couple the model to microscale descriptions, e.g. the explicit modeling of the extension of filopodia, the sensing antennas of the cell [2].

As cells migrate, they plough their way through a mesh of fibrous proteins (e.g. collagen, fibronectin and elastin). This extracellular matrix serves as a scaffolding along which cells can pull themselves forward. It also accommodates growth factors and other signaling proteins, which can exert highly localized biochemical cues on cells.
One key enrichment of the present model over many existing approaches, is the way it accounts for this extracellular matrix; the matrix consists of a random collection of lines, which interacts with the cell density through “cell-matrix” adhesion and by harboring growth factors (see Figures 1 and 2).
This advantage becomes clear when we apply the model to sprouting angiogenesis, the new formation of blood vessels from existing ones: in contradistinction to models using cellular automata based descriptions (e.g. McDougall et al. [3]), here the branching pattern of the vasculature is an output of the simulation, and not an imposed parameter. By virtue of this approach, we were for instance able to capture the increased branching as induced by matrix-bound growth factors [4].

[1] T. Werbowetski, R. Bjerkvig, and F. Del Maestro. Evidence for a secreted chemorepellent that directs glioma cell invasion. Journal of Neurobiology, 60(1):71–88, 2004.
[2] F. Milde, M. Bergdorf, and P. Koumoutsakos. A hybrid model for 3D simulations of sprouting angiogenesis. Biophys. J., submitted, 2007.
[3] M. Bergdorf, F. Milde, and P. Koumoutsakos. Mesoscale models of mesenchymal motion, in preparation, 2007
[4] S. R. McDougall, A. R. A. Anderson, and M. A. J. Chaplain. Mathematical modelling of dynamic adaptive tumour-induced angiogenesis: Clinical implications and therapeutic targeting strategies. Journal of Theoretical Biology, 241(3):564–589, 2006.

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From turbulence to tumor dynamics

using massively-parallel technology and multiresolution.

Fig 1: Simulation of avascular tumor growth using a continuum sharp-interface model. The dark areas denote necrotic tumor tissue.

Computing turbulent flows has doggedly remained one of the grand challenges of computational science. Due to the high complexity of turbulent flows, direct numerical simulations of such flows need to be performed on parallel machines and simulation codes need to be scalable. I have co-developed a highly scalable software library [2] for the simulation of general transport equations using particle methods. This open source library makes it possible to simulate problems ranging from solid tumor growth (Fig. 1) to aircraft wake flows [3],[ScienceDaily article] on massively-parallel architectures with tens of thousands of CPUs. However, even as massively-parallel computing architectures become affordable and increasingly accessible, we are still far from being able to perform direct calculations of many engineering flows, e.g. the air flow past a car.
Our efforts of breaking the complexity of such applications of computational science cannot solely rely on the steady advances in computing hardware, but must be complemented with the development of smarter algorithms.

I have been developing “smart” algorithms for tackling transport problems, that feature a broad range of spatial features [4,5]. The “Lagrangian Wavelet-Particle Method” is based on hybrid smooth particle methods: these serve as a robust and efficient foundation for solving transport equations in the Lagrangian frame. I extended this base framework by incorporating wavelet-based multiresolution analyses (MRA). Using principles reminiscent of wavelet techniques for image compression, these MRAs are performed on the physical quantities carried by the computational elements, and provide an adaptive distribution of numerical scales which effectively represent the physical scales using a hierarchy of resolutions. An extended formulation of this method pertaining to level set interface capturing problems introduced the first geometry-aware adaptation of level sets.
I demonstrated the versatility and enhanced accuracy of this approach by applying it to level set benchmark problems, where it compared favorably to state-of-the-art schemes [6], and to the simulation of crystal growth.

[1] M. Bergdorf, P. Koumoutsakos, and A. Leonard. DNS of vortex rings at Re=7,500. J. Fluid Mech., 581:495–505, 2007.
[2] I. F. Sbalzarini, J. H. Walther, M. Bergdorf, S. E. Hieber, E. M. Kotsalis, and P. Koumoutsakos. PPM – a highly efficient parallel particle-mesh library. J. Comput. Phys., 215(2):566–588, 2006.
[3] P. Chatelain, A. Curioni, M. Bergdorf, W. Andreoni, and P. Koumoutsakos. Billion Vortex Particle direct numerical simulation of aircraft wakes. Comput. Methods Appl. Mech. Engrg., accepted, 2007.
[4] M. Bergdorf, G.-H. Cottet, and P. Koumoutsakos. Multilevel adaptive particle methods for convection-diffusion equations. Multiscale Model. Simul., 4(1):328–357, 2005.
[5] M. Bergdorf and P. Koumoutsakos. A Lagrangian particle-wavelet method. Multiscale Model. Simul., 5(3):980–995, 2006.
[6] D. Enright, R. Fedkiw, J. Ferziger, and I. Mitchell. A hybrid particle level set method for improved interface capturing. J. Comput. Phys., 183(1):83–116, 2002.

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